Inelastic transport through molecules: comparing first-principles calculations to experiments

Toward Density-Functional Theory-Based Structure-Conductance Relationships in Single Molecule Junctions

A method is presented that allows for the calculation using density functional theory (DFT) of the tunneling conductance of single molecule junctions for thousands of junction structures. With a single scaling parameter, conductance is evaluated from clusters consisting of the molecule bonded to one Au atom at each end. Junction geometries are obtained without any constraints from ab initio molecular dynamics simulations at room temperature. This method accurately reproduces standard DFT-based conductance values for several molecular and electrode structures while reducing the computational cost by a factor of ∼400×, allowing for the conductance of tens of thousands of geometries to be computed. When applied to a pair of conjugated molecules, these large data sets quantify the effect on conductance of molecular structure or quantum chemical properties. This methodology enables reliable DFT-based conductance calculations at a negligible computational cost and opens the way to quantitative structure-conductance relationships.

Electronic transport through single-molecule oligophenyl-diethynyl junctions with direct gold-carbon bonds formed at low temperature

We report on the first systematic transport study of alkynyl-ended oligophenyl-diethynyl (OPA) single-molecule junctions with direct Au-C anchoring scheme at low temperature using the mechanically controlled break junction technique. Through quantitative statistical analysis of opening traces, conductance histograms and density functional theory studies, we identified different types of junctions, classified by their conductance and stretching behavior, for OPA molecules between Au electrodes with two to four phenyl rings. We performed inelastic electron tunneling spectroscopy and observed the excitation of Au-C vibrational modes confirming the existence of Au-C bonds at low temperature and compared the stability of molecule junctions upon mechanical stretching. Our findings reveal the huge potential for future functional molecule transport studies at low temperature using alkynyl endgroups.

Extending the source-sink potential method to include electron-nucleus coupling

The source-sink potential (SSP) method provides a simple tool for the qualitative analysis of the conductance of molecular electronic devices, and often analytical expressions for the conductance can be obtained. Here, we extend the SSP approach to account for decoherent, inelastic electron transport by including the non-adiabatic coupling between the electrons and the nuclei in the molecule. This coupling results in contributions to electron transport that can modify the qualitative structure-conductance relationships that we unraveled previously with SSP. In the approach proposed, electron-nucleus interactions are treated starting from the harmonic approximation for the nuclei, using a non-perturbative approach to account for the non-adiabatic coupling. Our method qualitatively describes experimentally observed phenomena and allows for a simple analysis that often provides analytical formulas in terms of the physical parameters of the junction, e.g., vibrational energies, non-adiabatic coupling, and molecule-contact coupling.

Effect of the linkage modes of thiolated ethynyl groups on the spin-dependent electronic transport properties in transition metal porphyrin molecular junctions

Using density functional theory and nonequilibrium Green's function method, the spin-dependent electronic transport properties of six transition metal porphyrin molecules (VP, CrP, MnP, FeP, CoP, and NiP), which are linked to gold electrodes through the thiolated ethynyl groups, are investigated. Two different linkage modes (beta linkage and meso linkage) of the substituted ethynyl groups on the porphyrin macrocycle are considered. The results show that the linkage mode of ethynyl groups plays an important role on the spin transport properties of the molecular junctions and the beta linkage is more favorable for the spin filtering efficiency of current than the meso linkages. The spin-up and spin-down energy levels show the different evolutions which is responsible for the difference of spin filtering efficiency between the two linkage modes. The computational results of total current show that the meso-linked molecular junctions have the better conductive performances than the beta-linked ones which may be caused by the different electronic transport paths.

Understanding and Engineering Phonon-Mediated Tunneling into Graphene on Metal Surfaces

Metal-intercalated graphene on Ir(111) exhibits phonon signatures in inelastic electron tunneling spectroscopy with strengths that depend on the intercalant. Extraordinarily strong graphene phonon signals are observed for Cs intercalation. Li intercalation likewise induces clearly discriminable phonon signatures, albeit less pronounced than observed for Cs. The signal can be finely tuned by the alkali metal coverage and gradually disappears upon increasing the junction conductance from tunneling to contact ranges. In contrast to Cs and Li, for Ni-intercalated graphene the phonon signals stay below the detection limit in all transport ranges. Going beyond the conventional two-terminal approach, transport calculations provide a comprehensive understanding of the subtle interplay between the graphene-electrode coupling and the observation of graphene phonon spectroscopic signatures.

Environment-assisted quantum transport through single-molecule junctions

Single-molecule electronics has been envisioned as the ultimate goal in the miniaturisation of electronic circuits. While the aim of incorporating single-molecule junctions into modern technology still proves elusive, recent developments in this field have begun to enable experimental investigation of fundamental concepts within the area of chemical physics. One such phenomenon is the concept of environment-assisted quantum transport which has emerged from the investigation of exciton transport in photosynthetic complexes. Here, we study charge transport through a two-site molecular junction coupled to a vibrational environment. We demonstrate that vibrational interactions can significantly enhance the current through specific molecular orbitals. Our study offers a clear pathway towards finding and identifying environment-assisted transport phenomena in charge transport settings.

Theoretical study of electron tunneling through the spiral molecule junctions along spiral paths

A theoretical study of electron transport in spiral-shaped molecules along spiral paths is executed by the first principles calculations.

Probing the local environment of a single OPE3 molecule using inelastic tunneling electron spectroscopy

We study single-molecule oligo(phenylene ethynylene)dithiol junctions by means of inelastic electron tunneling spectroscopy (IETS). The molecule is contacted with gold nano-electrodes formed with the mechanically controllable break junction technique. We record the IETS spectrum of the molecule from direct current measurements, both as a function of time and electrode separation. We find that for fixed electrode separation the molecule switches between various configurations, which are characterized by different IETS spectra. Similar variations in the IETS signal are observed during atomic rearrangements upon stretching of the molecular junction. Using quantum chemistry calculations, we identity some of the vibrational modes which constitute a chemical fingerprint of the molecule. In addition, changes can be attributed to rearrangements of the local molecular environment, in particular at the molecule-electrode interface. This study shows the importance of taking into account the interaction with the electrodes when describing inelastic contributions to transport through single-molecule junctions.

The inelastic electron tunneling spectroscopy of curved finite-sized graphene nanoribbon based molecular devices

The inelastic electron scattering properties of the molecular devices of curved finite-sized graphene nanoribbon (GNR) slices have been studied by combining the density functional theory and Green's function method.

Effects of the basis set and of the exchange-correlation functional on the Inelastic Electron Tunneling signatures of 1,4-benzenedithiol

The effects of the atomic basis set and of the exchange-correlation (XC) functional on the Inelastic Electron Tunneling (IET) spectra have been investigated by considering the prototypical 1,4-benzenedithiol molecule. These studies have been completed by tackling the reliability of the same methods for predicting the IR absorption spectrum of the same molecule. The main conclusions are (i) the B3LYP XC functional is suitable to predict the relative vibrational frequencies, (ii) provided a scaling factor is used, the root mean square error on the vibrational frequencies goes down to 18 cm(-1), (iii) triple-ζ basis sets and in particular the cc-pVTZ basis set is a good compromise between accuracy and computational needs, (iv) basis set effects on the IET intensities are larger than those of the XC functional, and (v) the cc-pVTZ, cc-pVQZ, and aug-cc-pVDZ basis sets provide consistent IET intensities.

Strong overtones modes in inelastic electron tunneling spectroscopy with cross-conjugated molecules: a prediction from theory

Cross-conjugated molecules are known to exhibit destructive quantum interference, a property that has recently received considerable attention in single-molecule electronics. Destructive quantum interference can be understood as an antiresonance in the elastic transmission near the Fermi energy and leading to suppressed levels of elastic current. In most theoretical studies, only the elastic contributions to the current are taken into account. In this paper, we study the inelastic contributions to the current in cross-conjugated molecules and find that while the inelastic contribution to the current is larger than for molecules without interference, the overall behavior of the molecule is still dominated by the quantum interference feature. Second, an ongoing challenge for single molecule electronics is understanding and controlling the local geometry at the molecule-surface interface. With this in mind, we investigate a spectroscopic method capable of providing insight into these junctions for cross-conjugated molecules: inelastic electron tunneling spectroscopy (IETS). IETS has the advantage that the molecule interface is probed directly by the tunneling current. Previously, it has been thought that overtones are not observable in IETS. Here, overtones are predicted to be strong and, in some cases, the dominant spectroscopic features. We study the origin of the overtones and find that the interference features in these molecules are the key ingredient. The interference feature is a property of the transmission channels of the π system only, and consequently, in the vicinity of the interference feature, the transmission channels of the σ system and the π system become equally transmissive. This allows for scattering between the different transmission channels, which serves as a pathway to bypass the interference feature. A simple model calculation is able to reproduce the results obtained from atomistic calculations, and we use this to interpret these findings.

Inelastic tunneling spectroscopy of gold-thiol and gold-thiolate interfaces in molecular junctions: the role of hydrogen

It is widely believed that when a molecule with thiol (S-H) end groups bridges a pair of gold electrodes, the S atoms bond to the gold and the thiol H atoms detach from the molecule. However, little is known regarding the details of this process, its time scale, and whether molecules with and without thiol hydrogen atoms can coexist in molecular junctions. Here, we explore theoretically how inelastic tunneling spectroscopy (IETS) can shed light on these issues. We present calculations of the geometries, low bias conductances, and IETS of propanedithiol and propanedithiolate molecular junctions with gold electrodes. We show that IETS can distinguish between junctions with molecules having no, one, or two thiol hydrogen atoms. We find that in most cases, the single-molecule junctions in the IETS experiment of Hihath et al. [Nano Lett. 8, 1673 (2008)] had no thiol H atoms, but that a molecule with a single thiol H atom may have bridged their junction occasionally. We also consider the evolution of the IETS spectrum as a gold STM tip approaches the intact S-H group at the end of a molecule bound at its other end to a second electrode. We predict the frequency of a vibrational mode of the thiol H atom to increase by a factor ~2 as the gap between the tip and molecule narrows. Therefore, IETS should be able to track the approach of the tip towards the thiol group of the molecule and detect the detachment of the thiol H atom from the molecule when it occurs.

Inelastic transport and low-bias rectification in a single-molecule diode

Designing, controlling, and understanding rectification behavior in molecular-scale devices has been a goal of the molecular electronics community for many years. Here we study the transport behavior of a single molecule diode, and its nonrectifying, symmetric counterpart at low temperatures, and at both low and high biases to help elucidate the electron-phonon interactions and transport mechanisms in the rectifying system. We find that the onset of current rectification occurs at low biases, indicating a significant change in the elastic transport pathway. However, the peaks in the inelastic electron tunneling (IET) spectrum are antisymmetric about zero bias and show no significant changes in energy or intensity in the forward or reverse bias directions, indicating that despite the change in the elastic transmission probability there is little impact on the inelastic pathway. These results agree with first principles calculations performed to evaluate the IETS, which also allow us to identify which modes are active in the single molecule junction.

Molecular electronic junction transport: some pathways and some ideas

When a single molecule, or a collection of molecules, is placed between two electrodes and voltage is applied, one has a molecular transport junction. We discuss such junctions, their properties, their description, and some of their applications. The discussion is qualitative rather than quantitative, and focuses on mechanism, structure/function relations, regimes and mechanisms of transport, some molecular regularities, and some substantial challenges facing the field. Because there are many regimes and mechanisms in transport junctions, we will discuss time scales, geometries, and inelastic scattering methods for trying to determine the properties of molecules within these junctions. Finally, we discuss some device applications, some outstanding problems, and some future directions.

Non-coherent transport in carbon chains

The effect of electron-phonon (e-ph) interaction on the conductance of carbon chains is investigated by a non-equilibrium Green's function technique combined with a four-orbitals-per-atom tight-binding Hamiltonian. The optimized structure of the chain is found to be the semiconducting polyyne type (···-C≡C-C≡C-···). Our results show that the conductance of a carbon chain attached to two fixed contacts decreases due to e-ph interaction, and this reduction is stronger for longitudinal phonon modes which decrease the hopping energy between carbon atoms. Study of individual phonon modes reveals that emission of longitudinal phonons is stronger than that of transverse modes at room temperature, while absorption of transverse phonons is dominant. Conductance at finite temperature is also studied by considering the overall phonon effects; this shows that the reduction of the conductance is stronger at higher temperatures. The results are explained on the basis of the unique features of the carbon chain band structure.

Bending of conjugated molecular wires and its effect on electron conduction properties

The electronic structure and electron transport properties of simple conjugated molecular wires like oligophenylene ethynylene (OPE) and oligophenylene vinylene (OPV) are studied under compression. If artificially confined to a given shorter length, the oligomers tend to bend and bending causes a loss in the overlap of the conjugated molecular orbitals. Theoretical modeling of electronic transport has been carried out for all undistorted and compressed OPE/OPV oligomers. OPV exists in step-like or V-like conformations and they have the same stability with very similar frontier molecular orbitals. The conductances of these molecular wires are calculated when inserted between two gold probes and the conductances for OPV are found to be comparable to OPE when the interfaces are same. The conductance decreases with bending due to the gradual loss in overlap of the molecular orbitals. It is also found that the conductances of the molecular wires decrease very strongly if the terminal sulfur atom is simultaneously bonded to hydrogen and a gold surface, thus reflecting the importance of the interface in determining the conductance in two-probe systems. From the conductance studies it may be concluded that if one or more benzene rings of OPE are rotated from coplanar conditions, the orthogonal molecular orbitals may completely block the electronic transport, rendering the molecule insulating.

Electron-phonon interactions in single octanedithiol molecular junctions

We study the charge transport properties and electron-phonon interactions in single molecule junctions, each consisting of an octanedithiol molecule covalently bound to two electrodes. Conductance measurements over a wide temperature range establish tunneling as the dominant charge transport process. Inelastic electron tunneling spectroscopy performed on individual molecular junctions provides a chemical signature of the molecule and allows electron-phonon interaction induced changes in the conductance to be explored. By fitting the conductance changes in the molecular junction using a simple model for inelastic transport, it is possible to estimate the phonon damping rates in the molecule. Finally, changes in the inelastic spectra are examined in relation to conductance switching events in the junction to demonstrate how changes in the configuration of the molecule or contact geometry can affect the conductance of the molecular junction.

Inelastic tunneling spectroscopy of alkanethiol molecules: high-resolution spectroscopy and theoretical simulations

We investigate inelastic electron tunneling spectroscopy (IETS) for alkanethiol self-assembled monolayers (SAM) with a scanning tunneling microscope and compare it to first-principles calculations. Using a combination of partial deuteration of the molecule and high-resolution measurements, we identify and differentiate between methyl (CH3) and methylene (CH2) groups and their symmetric and asymmetric C-H stretch modes. The calculations agree quantitatively with the measured IETS in producing the weight of the symmetric and asymmetric C-H stretch modes while the methylene stretch mode is largely underestimated. We further show that inelastic intermolecular scattering is important in the SAM by plotting the theoretical current densities.

Inelastic electron tunneling spectroscopy of single-molecule junctions using a mechanically controllable break junction

We report the use of electrical measurements to identify simultaneously the number and type of organic molecules within metal-molecule-metal junctions. Our strategy combines analyses of single-molecule conductance and inelastic electron tunneling spectra, exploiting a nanofabricated mechanically controllable break junction. We found that the peak linewidth of the inelastic electron tunneling spectrum decreased as the modulation voltage and temperature decreased, and that the selection rule for inelastic electron tunneling spectroscopy agrees with that for Raman spectroscopy. Furthermore, the differential conductance curve of the single-molecule junction suggests that it has asymmetrical electrode-molecule coupling.

Molecular modeling of inelastic electron transport in molecular junctions

A quantum chemical approach for the modeling of inelastic electron tunneling spectroscopy of molecular junctions based on scattering theory is presented. Within a harmonic approximation, the proposed method allows us to calculate the electron-vibration coupling strength analytically, which makes it applicable to many different systems. The calculated inelastic electron transport spectra are often in very good agreement with their experimental counterparts, allowing the revelation of detailed information about molecular conformations inside the junction, molecule-metal contact structures, and intermolecular interaction that is largely inaccessible experimentally.

Inelastic electron tunnelling in saturated molecules with different functional groups: correlations and symmetry considerations from a computational study

The inelastic electron tunnelling (IET) spectra of a series of molecules with the commonest functional groups are evaluated computationally. It is found that ether, secondary amine and thioether groups do not leave any characteristic signatures on the IET spectrum (in comparison with simple alkanes) and they cannot be used as 'tracers' for the tunnelling path of the electron. In contrast, carbonyl and ester groups modify the appearance of the IET spectrum considerably. The series of computations was also used to validate, for the case of saturated molecules, the propensity rules for IET spectroscopy proposed in the literature. It is found that totally symmetric vibrations give the largest contribution to the spectrum and that there is no correlation between IET and infrared or Raman absorption intensities.

Length-dependent conductance of molecular wires and contact resistance in metal-molecule-metal junctions

Molecular wires are covalently bonded to gold electrodes--to form metal-molecule-metal junctions--by functionalizing each end with a -SH group. The conductance of a wide variety of molecular junctions is studied theoretically by using first-principles density functional theory (DFT) combined with the nonequilibrium Green's function (NEGF) formalism. Based on the chain-length-dependent conductance of the series of molecular wires, the attenuation factor beta is obtained and compared with the experimental data. The beta value is quantitatively correlated to the molecular HOMO-LUMO gap. Coupling between the metallic electrode and the molecular bridge plays an important role in electron transport. A contact resistance of 6.0+/-2.0 Kohms is obtained by extrapolating the molecular-bridge length to zero. This value is of the same magnitude as the quantum resistance.

Unified description of inelastic propensity rules for electron transport through nanoscale junctions

We present a method to analyze the results of first-principles based calculations of electronic currents including inelastic electron-phonon effects. This method allows us to determine the electronic and vibrational symmetries in play, and hence to obtain the so-called propensity rules for the studied systems. We show that only a few scattering states--namely those belonging to the most transmitting eigenchannels--need to be considered for a complete description of the electron transport. We apply the method on first-principles calculations of four different systems and obtain the propensity rules in each case.

Inelastic electron tunneling spectroscopy of an alkanethiol self-assembled monolayer using scanning tunneling microscopy

We report inelastic electron tunneling spectroscopy (IETS) of a C8 alkanethiol self-assembled monolayer using a scanning tunneling microscope (STM). High-resolution STM IETS spectra show clear features of the C-H bending and C-C stretching modes in addition to the C-H stretching mode, which enables a precise comparison with previously reported vibrational spectroscopy, especially electron energy loss spectroscopy data. Intensity variation of vibrational peaks with tip position is discussed with the STM IETS detection mechanism.

Systematic study on quantum confinement and waveguide effects for elastic and inelastic currents in atomic gold wire: importance of the phase factor for modeling electrodes

Quantum confinement of the electrodes is an important issue for electron transport through molecular or atomic wire junctions. To assess the importance of waveguide effects by quantum confinement of the electrodes, we have calculated elastic and inelastic conductance and inelastic electron tunneling spectra of atomic gold wire with gold electrodes for several models. The results show the quite important role of the phase factors between the modeled electrodes and the contact region.